No less than 12 hours before making ice cream, make sure the bowl of your ice cream maker has been in the freezer. You shouldn't be able to hear any liquid sloshing in the bowl.
In a food processor, pulse the pecans and almonds until they are roughly chopped. Remove from bowl and set aside.
Combine the remaining ingredients in the food processor, processing until smooth and uniform.
Following the manufacturer's instructions, pour the coconut milk mixture and chopped nuts into the ice cream machine, and let it churn for 25-30 minutes, or until thick.
About 5 minutes before the ice cream seems finished, add the broken-up graham crackers to the ice cream, and let combine.
Once ice cream is finished, either serve right away or pour into a freezer-safe air-tight container and let freeze.
To serve once frozen, let ice cream set out on the counter for about 30 minutes before scooping out.